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The sum sum ( k = 1 ) ^ ( 20 ) k ...

The sum ` sum _ ( k = 1 ) ^ ( 20 ) k ( 1 ) / ( 2 ^ k ) ` is equal to ` l - (11) /(m ^ ( 19 )) `. The value of ` ( l + m ) ` is ______ .

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To solve the given problem, we need to evaluate the sum \[ S = \sum_{k=1}^{20} k \cdot \frac{1}{2^k} \] and express it in the form \( l - \frac{11}{m^{19}} \) to find \( l + m \). ...
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